The present invention is concerned with a method and a unit for analytical model formulation, and is particularly concerned with a method and a unit for the formulation of an analytical model used for numerical analysis, such as the finite element method. The present invention is also concerned with the structure of the analytical model data, and with a program for analytical model formulation.
A conventional analytical model used for numerical analysis (such as the finite element method) was made using a tetrahedral, (pentahedral), hexahedral element for dividing a shape model defined by CAD into fine elements, which is referred to as element division. In the case of using a tetrahedral element, the element division could be automatically done. However, because a poor analytical accuracy was obtained using the tetrahedral element, it was not preferred. A good analytical accuracy was obtained using a hexahedral element, but element division could not be done automatically. Therefore, research on the dividing position was first undertaken, then each hexahedral element was obtained by manual division.
Use was made of method involving conversion of the shape models defined by CAD to the groups of rectangles referred to as voxel data, and used as hexahedral elements for numerical analysis. Element division could be done automatically with the method. A method for the formulation of voxel data from CAD data was disclosed in Japanese Kokai Patent Application No. Hei 8[1996]-153214.
However, in the above-mentioned conventional examples, because the analytical models were made using a rectangular shaped elements having structure similar to the hierarchical structure, fine rectangles (voxels) had to be used to improve the analytical accuracy, so the number of elements, which was so large that no conventional analytical processing units (software for analysis) could be used for analysis, as well as the size, which could be analyzed, were limited. There were analytical processing units that could be used to analyze an analytical model with the significantly large number. However, as the number of elements increased, the number of computations had to be increased, resulting in reduction of a processing speed.
The objectives of the present invention are to solve the problems of the above-mentioned conventional examples, and to provide a method and a unit for the formulation of an analytical model that can be analyzed using a conventional analytical processing unit while automatic element division is performed using voxel data. Another objective of the present invention is to provide analytical model data that can be used for quick analysis using hexahedral elements while maintaining analytical accuracy.
Data referred to as an octree is formulated using voxel data as the origin; the octree is used for the formulation of an analytical model in the present invention. Voxels contain and use the following data, i.e., whether a three-dimensional orthogonal lattice (=rectangle) is located inside or outside of the shape data, to display a certain shape. Because a rectangle [rectangular data] displaying a certain shape can be easily converted to an analytical model by directly using the rectangle as a hexahedral element, element division can be automated. However, because a significantly large amount of fine rectangles has to be used to reproduce the details of the original shape, the number (about 190,000 elements) of elements required for analysis using a conventional analytical processing unit may exceed the number of elements that could be processed using a conventional analytical processing unit.
An octree can display a shape using fewer rectangles than the voxel. The number of elements can be reduced using the rectangles of the octree as hexahedral elements, compared with the formulation of an analytical model using voxel data. Hierarchical voxel data are obtained by increasing each rectangle to twice the size, using the previously computed voxel data as the finest element. An analytical model is formulated using the hierarchical voxel data as octree data.
In the case of using neighboring elements having different sizes, a hexahedral element with 20 nodes is used as a large element to maintain the connection between the elements used to formulate an analytical mode. The free nodes between neighboring elements are constrained. When octree data are formulated, a hierarchy with 1 level is maintained to obtain a difference of 1 level or less in size between neighboring elements.
Therefore, the present invention has the following configuration. A voxel data reading process used to read voxel data on the shape of an object of analysis that is defined by the groups of rectangles of voxels [rectangular voxel data]; boundary determination process used to determine whether each voxel contained in the voxel data, which is read in the voxel data reading process, belongs to a boundary separating the inside from the outside of the shape of the above-mentioned object of analysis; a connected voxel determination process used to recursively determine whether the voxel at each level is connected to the other voxel that is determined to be located at the boundary at the boundary determination process; and a voxel redefinition process used to redefine each voxel at each level in the groups determined, in the above-mentioned connected voxel determination process, to be the voxels at each level that are several times wider than the rectangular voxels determined to be located at the boundary in the above-mentioned boundary determination process. The above-mentioned objective is completed by such a configuration.
In the method for analytical model formulation of the present invention, voxel data, which have been previously formulated, are read. The voxels that are located at the boundary or are connected to the boundary are then examined among many voxels. In the case of the outermost layer of voxel data read and located inside the boundary, it was determined that the voxels in the outermost layer are located at the boundary. In the case of the outermost layer located at the boundary, the voxels in the outermost layer are located at the boundary. The outermost layer appears on the surface of the shape of object of the analysis. In the connected voxel determination process, a connection between the voxels located at the boundary through the innermost layer is determined for each level. If the voxels located at the boundary are referred to as level 1, it is determined that the voxels connecting to the voxels in level 1 only are referred to as level 2. The voxels connected to level 2 only are referred to as level 3. In the voxel redefinition process, the voxels located at the boundary are redefined and referred to as the smallest ones. The voxels of all voxel connection levels are redefined according to the levels to obtain octree data. As the width of a rectangle is used to obtain the difference in size between the voxels, a good connection can be easily obtained between the voxels with different sizes.
Analytical model data having the following structure are obtained using a method and a unit for analytical model formulation of the present invention. The analytical model data have the hierarchical structure containing the first level voxels that are located at the boundary separating the inside from the outside of an object of analysis, the second level voxels that are connected to the first level voxels and are wider than the first level voxels, and the n-level voxels that are connected to the m-level voxels and are wider than the m-level voxels. The n-level voxels define nodes connecting to the vertices of the m-level voxels, and contain constraining data used to constrain the nodes at the vertices of the m-level voxels. The analytical model data can be read and analyzed by a computer used for structural analysis of the shape of an object of analysis. The analytical model data are stored in any storage medium and sent to the computer.
Because the groups of voxels showing the shape of an analytical model are hierarchically defined by voxel data consisting of several levels including the first level voxels that belong the surface (boundary) of a shape analyzed in the present invention, in other words, octree data, the computing steps required for analysis using a computer can be reduced due to the small number of octree data when analytical model data are read by a computer, and because small voxels are located near the surface of a shape analyzed in the present invention, a certain analytical accuracy can be maintained, and because analytical model data define nodes connected to the vertices of the m-level voxels and contain constraining data used to constrain the nodes at the vertices of the m-level voxels in the present invention, the structural accuracy is not reduced by defining the shape of a structure using octree data since small voxels are constrained by large voxels at the nodes. Therefore, the present invention can solve the above-mentioned problems.